## EVENT DETAILS AND ABSTRACT

**Interdisciplinary Seminar in Nonlinear Science**
**Title:** Competition in Phase Synchronization of Chaotic Attractors & Indeterminate Saddle-Node Bifurcation

**Speaker:** Romulus Breban

**Speaker Info:** University of Maryland

**Brief Description:**

**Special Note**: **More current information may be available at Plan-it Purple**

**Abstract:**

In this talk two different topics in dynamical systems will be discussed:

1)the competition between two periodic signals in phase synchronization of chaotic attractors when a the system is driven with two frequencies. There are several possible motivations for this study. First, there may be real situations where a chaotic dynamical system simultaneously receives inputs from two distinct periodic systems (e.g., a neuron receiving signals from two other neurons). Second, the study of a signal with two frequencies can be regarded as the next step from the single frequency case in understanding phase synchronization of chaos by signals with nontrivial frequency power spectra. Third, this situation is a generalization of the problem in which two periodic signals compete to entrain a nonlinear periodic oscillator.

2) the scaling properties of the indeterminate saddle-node bifurcation for a slowly swept control parameter and in the presence of noise.

We consider systems that depend slowly on time (i.e., they drift) in such a way that the system slowly sweeps through a saddle-node bifurcation. Due to a common type of fractal basin boundary structure, such situations can often be expected to be ``indeterminate'' in the sense that it is fundamentally difficult to predict the eventual fate of an orbit that tracks the pre-bifurcation node attractor. We study the scaling properties of this indeterminacy; specifically, the sensitive dependence of the orbit's final attractor on the sweeping rate, and the scaling with noise amplitude of the final attractor capture probability.

**Date:** Thursday, June 26, 2003

**Time:** 11:00AM

**Where:** Tech M416

**Contact Person:** Hermann Riecke

**Contact email:** h-riecke@northwestern.edu

**Contact Phone:** 847-491-8316

Copyright © 1997-2024
Department of Mathematics, Northwestern University.